Change of Scaling and Appearance of Scale-Free Size Distribution in Aggregation Kinetics by Additive Rules

摘要

The idealized general model of aggregate growth is considered on the basis ofthe simple additive rules that correspond to one-step aggregation process. Thetwo idealized cases were analytically investigated and simulated by Monte Carlomethod in the Desktop Grid distributed computing environment to analyze"pile-up" and "wall" cluster distributions in different aggregation scenarios.Several aspects of aggregation kinetics (change of scaling, change of sizedistribution type, and appearance of scale-free size distribution) driven by"zero cluster size" boundary condition were determined by analysis of evolvingcumulative distribution functions. The "pile-up" case with a \textit{minimum}active surface (singularity) could imitate piling up aggregations ofdislocations, and the case with a \textit{maximum} active surface could imitatearrangements of dislocations in walls. The change of scaling law (for pile-upsand walls) and availability of scale-free distributions (for walls) wereanalytically shown and confirmed by scaling, fitting, moment, and bootstrappinganalyses of simulated probability density and cumulative distributionfunctions. The initial "singular" \textit{symmetric} distribution of pile-upsevolves by the "infinite" diffusive scaling law and later it is replaced by theother "semi-infinite" diffusive scaling law with \textit{asymmetric}distribution of pile-ups. In contrast, the initial "singular"\textit{symmetric} distributions of walls initially evolve by the diffusivescaling law and later it is replaced by the other ballistic (linear) scalinglaw with \textit{scale-free} exponential distributions without distinctivepeaks. The conclusion was made as to possible applications of such approach forscaling, fitting, moment, and bootstrapping analyses of distributions insimulated and experimental data.